Counting the number of distinct real roots of certain polynomials by Bezoutian and the Galois groups over the rational number field

Shuichi Otake

    研究成果: Article

    抄録

    In this article, we count the number of distinct real roots of certain polynomials in terms of Bezoutian form. As an application, we construct certain irreducible polynomials over the rational number field which have given number of real roots and by the result of Oz Ben-Shimol [On Galois groups of prime degree polynomials with complex roots, Algebra Disc. Math. 2 (2009), pp. 99-107], we obtain an algorithm to construct irreducible polynomials of prime degree p whose Galois groups are isomorphic to Sp or Ap.

    元の言語English
    ページ(範囲)429-441
    ページ数13
    ジャーナルLinear and Multilinear Algebra
    61
    発行部数4
    DOI
    出版物ステータスPublished - 2013 4

    Fingerprint

    Irreducible polynomial
    Real Roots
    Galois group
    Number field
    Counting
    Distinct
    Polynomial
    Count
    Isomorphic
    Roots
    Algebra
    Form

    ASJC Scopus subject areas

    • Algebra and Number Theory

    これを引用

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    KW - Galois group

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